Multiple Path Finding System for Replacement Tasks - Science Direct

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ScienceDirect Procedia CIRP 33 (2015) 3 – 8

9th CIRP Conference on Intelligent Computation in Manufacturing Engineering - CIRP ICME '14

Multiple Path Finding System for Replacement Tasks Atsuko ENOMOTO(3)a*, Norisuke FUJII(3)a, Yoichi NONAKA(3)a, Juergen RASCHb, Sonja SCHULTEb, Michael ENGELHARDTb, Joerg KOLIBABKAb Jun'ichi KANEKOc, Tsukasa ICHIJOc, Kyohei SHIBUTAc a b

Hitachi, Ltd., Yokohama Research Laboratory (3), Yokohama, Japan Mitsubishi Hitachi Power Systems Europe GmbH, Duisburg, Germany c Saitama University, Saitama, Japan

* Corresponding author. Tel.: +81-80-9353-9877; fax: +81-50-3135-3412. E-mail address:[email protected]

Abstract Planning alternative multiple carry-in/out paths is essential to the engineering work of replacement tasks in power plant maintenance, adapting to the uncertain 3D environment of the plant building. For this subject, dissimilarity of the planned paths and fast response time for the query are required for a path finding algorithm. Existing path finding algorithms can find exact multiple paths but the differences of found paths are very little. Besides, the computation times are not feasible for a large volume of 3D space such as power plant. In this paper, a novel multiple paths finding algorithm is proposed for dissimilar paths planning with fast response time for the query, realizing interactive operations. Furthermore, performance indices for the path finding is designed with consideration of secure carry-in/out operations in the proposed algorithm. The algorithm outputs crane suspension trajectory avoiding collision with the plant building. The system has been applied to replacement tasks of an existing boiler building of a power plant. The building is expressed by over 5 GB stereo-lithography binary data. © Authors. Published by Elsevier © 2014 2014 The Published by Elsevier B.V. This is anB.V. open access article under the CC BY-NC-ND license Peer-review under responsibility of the International Scientific Committee of “9th CIRP ICME Conference". (http://creativecommons.org/licenses/by-nc-nd/4.0/). Selection and peer-review under responsibility of the International Scientific Committee of “9th CIRP ICME Conference” Keywords: Digital Manufacturing System; Virtual reality; Plant maintenance; Path finding; Path planning; Trajectory generation.

1. Introduction Power plant constructors maintain the performance of plant by health diagnosis and replacements of components. The maintenance business becomes one of the important revenue sources for the constructors because profit rate of maintenance business is much higher than that of new power plant construction. Furthermore, maintenance business becomes more and more important to constructors in the context of growing number of power plant deterioration in advanced countries. The competition of the maintenance business becomes intensified recently. Competitive price setting of maintenance is crucial to get a maintenance contract from electric power companies. Therefore, cost reduction of maintenance tasks is quite important. For the cost reduction of health diagnosis, conventional health diagnosis with hammering test for pipe corrosion gave place to multiple on-

line sensing temperatures, pressures and vibrations. This reduces cost of diagnosis processes in maintenance. For the cost reduction of replacement tasks, on demand planning of accurate carry-out or carry-in(carry-out/in) paths is very important. Accurate path means having no collision with the power plant building structures, machinery and equipment. For the collision check, conventional 3D-CAD systems have been utilized in which, engineers has to develop paths manually. It is not on demand because it takes five hours for one path for carrying in a boiler plant building for instance. The manually planed carry-out/in paths are not accurate due to overlook of collision occurrences. It appears that the paths are not feasible on site. This induces the rework of the carry-out/in tasks. The rework consumes resources of workers and equipment therefore it is one of main reason of incensement of the cost of replacement tasks. If one complete carry-out/in path is planned, it is not

2212-8271 © 2014 Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Selection and peer-review under responsibility of the International Scientific Committee of “9th CIRP ICME Conference” doi:10.1016/j.procir.2015.06.003

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sufficient for replacement tasks in the site of power plant buildings. The reason is, it some times exists unexpected equipment or building structures which are not expressed as 3D models. These un-modelled obstacles cause unexpected collision in the site. Planning of alternative paths can adapt to these unexpected situations. Besides, these paths should be very dissimilar to each other in order to become alternative. In this paper, a novel path finding algorithm on a graph network for planning of carry-out/in tasks in plant buildings is proposed. There are two important respects to find carryout/in paths for replacement tasks in a plant building. The one is size of corner space for direction change of the carried component. In carry-out/ in work, components are suspended by overhead cranes because most components weigh more than a ton. Workers manipulate the crane to change direction of the suspended component in each corner. Each corner needs to be large enough to rotate the component without collision, the sizes of components are several meters. In power plants, large spaces are reserved for direction change of suspended components. An example of large spaces is the entrance of ‘erection shaft’ that is a space for lifting up or down components. In this paper, such spaces for changing direction of components are called as 'turning point' and largeness of space is called as 'space margin'. The other one is the number of turning points. Fewer turning points are preferable from the view point of cost of the crane operations. Because each direction change of the suspended component require a long operational time. Besides, many travel rails for the crane increase the cost also. Remaining crucial subject is position and posture trajectory generation with collision avoidance in turning points. Detailed trajectories including postures should be simulated in advance of actual crane operations. At turning points, carne operations tend to be reworked because of unexpected collision occurrences. Motion of the carry-out/in component is constrained by kinematics of the crane suspension. There are two different types of kinematics in crane suspension; one is for horizontal corner and the other is for vertical corner. In this paper, dynamic motion of the component suspended by crane is calculated considering with automatic modification to avoid collision with the environment. This paper consists of 7 sections. Related works are discussed in section 2. The goals and approaches to the research target are described in section 3. Multiple paths finding algorithm is proposed in section 4. Collision avoidance trajectory generation at turning points are proposed in section 5. Feasibility of found paths is verified in section 6. Section 7 concludes our research. 2. Related works Path finding for carry-out/carry-in tasks of power plants had been experimentally conducted by on-site supervisors. Recently, off-site path planning for carry-out/carry-in tasks becomes possible because of advancement of 3D-CAD systems[1][2][3][4][5][6]. These commercialized systems provide realistic environment engineers to plan carry-in/carryout paths with trial and error. The problem of the path planning process of trial and error consumes long time for

instance five hours per one path for finding one feasible path. In the early days of the research, some methods are proposed in the research field of graph theory. Graph theory has been developed to solve mathematical problem such as Konigsberg bridge problem. Graph theory formulates various problems using graph with nodes and edges. A node indicates a certain condition of the problem (e.g., position of carryout/carry-in component in 3 dimensional spaces, a combination of data) and an edge indicates connectivity between two nodes. One of the most popular problems in graph theory is the shortest path problem. In the problem, a goal is to find the shortest path from a start node to a goal node. To solve the shortest path problem, Dijkstra proposed a fundamental method in 1959 [7]. This method has been improved up to the present time. Most of the improvements are focused on the adjustment of data structure. For example, Fibonacci heap is able to shorten calculation time of Dijkstra method. A* method is a sort of modification of Dijkstra method [8]. And A* utilizes estimation value to select desirable nodes. These methods are utilized in various commercialized systems such as car navigation systems, robot motion planning systems etc. The subject of the shortest path problem is also diversified such as k-shortest path problem. The goal of K-shortest path problem is to find not only the shortest path, but also K other shortest paths. With recent methods, k-shortest path problem is solved in nearly the order of square of the number of nodes (namely, size of search space) in worst case [9]. However it is not enough to automatic carry-out/carry-in path finding for plant structures because obtained paths are not different enough to utilize different situations. That is, since the obtained paths go along most of the same trajectory, all the paths become useless in the case a part of the paths is occupied by equipment or building structures which are not modeled in 3D space of path finding. This research also proposes a path finding algorithm based on heuristic approach. A challenging point of our research is to find dissimilar multiple paths considering space margin which is not considered in previous studies. One of technical features for applying graph theory to the issue of path finding is conversion of 3D space geometric data to a graph network. This conversion is called as preprocess in this area. Preprocess methods which converts geometric data to graph structure have been researched mainly in the area of robotics. Lozano and Wesley proposed an idea of configuration space to build graph structure from geometric data [10][11]. A configuration space is a set of free spaces with respect to joint space of the robot where no interference is occurred between robot and the environment. The configuration space is converted into a graph by some dividing method of configuration space. In this paper, a new preprocess method is proposed for generation of a graph network focused on the problem of carry-out/in path finding. Automatic path finding in a 3 dimensional space is called as "piano movers problem" [12]. The problem is solved by graph theory and building methods of configuration space. Path finding in 3 dimensional configuration spaces requires a

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heavy calculation cost even if graph is given. Therefore, most of recent path finding algorithms adopt heuristic approaches [13] or probabilistic approaches to reduce calculation cost [14][15][16]. Our proposing method is also located on heuristic approaches. Another technical subject to realize carry-out/ in task is posture of the component. In the task, overhead cranes are utilized to carry the component for the motion in a horizontal plane and the motion of lifting up/ down. The position and the posture of the carry-out/ in path are constrained by the overhead crane kinematics and the operation rule for worker's safety. However, Few studies of path finding for overhead crane consider the posture, likely the suspended components are assumed as a ball [17]. Some studies propose utilization of multi-body dynamics but do not pay attention for collision avoidance[18]. Regards to planning trajectories of the position and the posture(pose), multi-body dynamics has been employed in various areas. For instance, car dynamics models are installed in an urban traffic model in intersections to reproduce realistic traffic simulation[19]. In robotic area including AGV (Automated Guided Vehicle), many studies adopt configuration space[20][21] which is not feasible for large size of 3D space. Our research proposes a novel method of trajectories generation of pose for collision avoidance during crane suspension with multi-body dynamics. 3. Requirements and Algorithm Overview 3.1. Requirements The goal of this research is to develop a multiple paths finding algorithm satisfying three requirements; (1) To realize interactive operations, the allowable computation time for one path finding is specified as 1 minute. The time does not include pre-process time for generation of the graph network. (2) The paths travel dissimilar course each other to provide alternative plans for the user. The sizes of space margins and the number of turning points are utilized as the performance indexes of path finding. (3) generation of the pose trajectories avoiding collisions in crane suspension. Figure 3.1 shows an application target of our system where (a) indicates 3D-CAD models of an existing boiler plant. The size is over 5GB as STL binary data. A picture of crane operation in an erection shaft is shown in (b) in Fig. 3.1. 3.2. Algorithm overview In piano mover problem, collision avoidance postures are searched in the configuration space. However, the approach is not feasible for posture finding of the suspended component in a plant space because of largeness of the size and complexity of the 3D data of the plant model. Therefore many studies take the assumption that the suspended component is a ball or mass point which does not need consideration of the posture. Compatibility of path finding and trajectory

(a) 3D CAD data of power plant

(b) Crane operation

Fig 3.1 Overview of carry-out/in operation

Inputs: STL models & start and end point Multiple paths finding sequences of turning points Pose calculation around turning points Collision check Collide?

No

Yes

Revise of kinematic parameter of crane Outputs: Animations & work instruction sheets Fig 3.2 Flow chart of fast automatic path planning tool system

generation for crane suspension is one of the crucial subjects in this research. In crane work, suspended posture is constant in prismatic motion and the posture is only changed around turning points. This means trajectories of prismatic motion and that of rotational motion are possible to be generated independently. According to this feature, we propose path finding algorithm with two steps. The first step is multiple paths finding assuming that component is a mass point. The performance indexes of path finding are space margins and the number of turning points. The second step is pose calculation of the component considering kinematic models of crane suspension. Crane suspension trajectory around every turning point is calculated considering collision avoidance. In case of any collision occurrence, the kinematic parameters of crane suspension are revised and trajectory is re-generated. Finally, animation and work instruction sheets are generated as outputs. Flow chart of the developed system is shown in Fig.3.2. The inputs of this system are STL data of building structures including components to carry and a pair of start point and end point of paths to find. The system outputs animations of carry-out/carry-in paths and the work instruction sheets. 4. Multiple paths finding considering space margin Three requirements are listed up in section 3. To meet the requirement (1) and (2), we decompose multiple dissimilar

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paths finding problem into iterative single path finding problem. This decomposition is achieved by adopting Dijkstra's algorithm for single path finding and constraining travelable path iteratively in descending order of performance indexes of paths finding. Approach proposed here achieves the order of O(kn2) which is equivalent to original Dijkstra's algorithm multiplied by the number of found paths where n is the number of the spaces and k is the number of paths. In addition, paths created in this approach are quite dissimilar by virtue of constraint of travelable spaces in each iteration. For the requirement (2), our algorithms give priorities to following indexes. Priorities of the performance indexes are decided from discussions with power plant construction engineers as follows. (1) The number of turning points. The more number of turning points exist, operation cost becomes higher and moreover the production cost is added because the more travel rails for crane suspensions are required. (2) Space margin. The larger space margin becomes, the easier carry-out/in operation becomes then the operation cost is reduced, especially rotation in turning points. (3) Path length. The smaller path length becomes, the shorter carry-out/in operation time becomes, namely the operation cost decreases. According to this key idea, the following algorithm is newly developed. Step 1. Plant 3D-CAD model is divided into many rectangular solids called voxels. This process divides a voxel into eight voxels (i.e., octree) if the voxel includes building structures and size of the voxels are more than predefined minimal size. Step 2. In every voxel, the space margin is calculated as distances from center of voxel to the nearest point of the building structures. Every space margin is registered as characteristics of the each voxel. Step 3. All voxels are divided if the size is more than predefined minimal size. Every divided voxel inherits the space margin from the original voxel. Step 4. Graph network is structured by voxels. In the graph network, a node indicates a voxel and an arc indicates adjacency between two voxels. However, It is not allowed to connect two voxels located in upper and lower oblique direction because crane cannot transfer suspended component up or down obliquely. Each node has its space margin registered in Step 3. Step 5. The first path is found by Dijkstra's algorithm. Step 6. A voxel with the largest margin, among voxels in which, the found path goes through, is erased and the network of the graph is modified accordingly. Step 7. Step 5 and 6 are repeated until all paths of required number are found. Figure. 4.1(a) indicates an example of 3D-CAD model. Figure 4.1(b) indicates a result of Step 2. White boxes in the left part indicate voxels and deep blue circles in the right part indicate nodes. Left part of Fig. 4.1(c) indicates result of step 3 and the right part indicates the graph network of Step 4. Figure 4.1(d) shows result of Step 5. Green boxes denote start and end point. Red line indicates a found path. Figure. 4.1(e) indicates result of Step 6. Figure 4.1(f) shows result of Step 7.

End

Start

(a) An image of plant structure

(d) First path creation

Space margin 2 11 2

Space margin 2 11 2

1 1

1 1

1 1

2

11

2

2

(b) Free space octants

11

2

(e) Graph modification End

Space margin 2 11 2 1 1

1 1

1 1 2

11

(c)Graph network

2

Start

(f) Modified graph and 2nd path

Fig. 4.1 Multi-path planning with automatic work space recognition

cyan line indicates the second path. 5. Suspended posture calculation In the proposed path finding algorithm of section 4, the carry-out/carry-in component is assumed as a mass point without posture consideration. In crane work, suspended posture is constant in prismatic motion. Therefore, the assumption of the mass point is feasible if enough space margin is secured by the path finding algorithm in prismatic motion. Although, suspended posture is changed around every turning point for the direction change. In order to acquire suspended postures in turning points, this section proposes a method of pose trajectory generation with collision avoidance. In order to generate suspended postures by crane, two types of carne suspension kinematic model are proposed as shown in Fig. 5.1. In Type 1, the component is suspended by two links connected with spherical joints and hung on horizontal rails with two prismatic joints. The rails are crossing over and the suspended component is switched from one rail to another in order to change its direction. in Type 2, the component is suspended by one link connected with one spherical joint and hung on vertical rail with a spherical joint to lift up or down along the vertical rail. Dynamics equation is expressed as a differential algebraic equations as below;

º F ª M O )Tv º ªV º ª « » « » T »« c c c c J c ): » : (5.1) «O « » «N  : J : » » «) v ) : O » «¬ / »¼ « ) ¬ ¼ ¬ ¼ where M is mass matrix and J c is inertia tensor matrix of links. ) v and ) : are kinematic constraints matrixes of prismatic and rotational accelerations terms respectively. ) R is other remaining terms of kinematic constraints. F in equation(5.1) is outer forces vector affected in each R

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V and : are prismatic and rotational acceleration vectors of the links respectively. / is Lagrange multipliers vector. By solving dynamics equation (5.1), the positions and postures of suspended component are derived in time series. Figure 5.2 (b) shows the generated poses of the Type 1. In the case of collision, modification of the neighbour waypoints may decrease some space margins in the path. In the same way, adding any new turning points increase the number of the turning points of the path. There is another way to avoid collision without side effect to the performance of the path. We noticed the kinematical parameters of suspension models those can be changed without any side effects to space margin and the number of turning points. Figure 5.3 expresses the position trajectories of the Type 1 for four values of kinematic parameter d1. d1 denotes distance between two suspension points in the Type1 shown in Fig.5.1. The trajectory goes more internal side of the turning point according to decrease of d1. Larger distance of suspension points can hold the component posture stable against outer force. Therefore trial of collision check starts with largest d1ˊ d1 is decreased to the smallest value (d1>0) while collision occurs in the trajectory. The trajectory without collision is employed as the trajectory of each turning point. For the Type 2, d2 is changed to check collision of trajectories in the same manner. In the case of the lower side of component collides, d2 is decreased until it does not collide. On the other hand, the upper part of the component collides; d2 is increased until it does not collide.

P S

Rail 2 Rail 1

P

links including gravity force g  R3 . For Type 1, a force f  R3 parallel to rail 2 is applied to link 2 in order to move suspended component along two rails as shown in Fig. 5.2. The outer forces vector is ; (5.2) F [ gT ( g  f )T gT ]T . For Type 2, outer forces vector for two links is only gravity force is considered as F [ gT gT ]T .

P

Link 1

S

Prismatic joint Spherical joint

Link 2

Link 1

Applied force f

S d1 Link 3 (a) Type 1

S

d2

S

Link 2

Gravity force g (b) Type 2

Fig. 5.1 Kinematic models of crane suspension

(b)Type 2:One point suspension (a)Type 1: Two rails suspension Fig 5.2 Pose trajectory

6. Application Results Proposed algorithm is evaluated by computational experiment using 3D data of an existing boiler building which size is 5.6GB in binary STL. The evaluation is executed by PC with Intel Core i7-3930k 3.2GHz CPU, 32.0GB RAM and NVIDIA Tesla C2075 graphic board. Collision check is implemented as parallel processing on the graphic board. Calculation times are evaluated by 25 found paths applying to the boiler building. Average pre-processing time is 16.4 seconds in which 3D-CAD model is divided into voxels and space margins are evaluated. The average times for a path finding and suspended poses of waypoints are 16.0 seconds and 3.8 seconds respectively. In total, for path finding and pose generation for one path is 26 seconds. This result is less than one minute which is specified as maximum time. Figure 6.1 shows an application results. In this case, five paths are found for a pair of start/end points to carry-in a pipe. Each path goes through different floors and different erection shafts. For an example, #1 and #2 go through a long erection shaft, while others go through two short erection shafts. Table 6.1 indicates a path evaluation result by 3 indexes. To

Turning point

Fig. 5.3 Type 1 pose trajectory trials for collision avoidance

evaluate dissimilarity of paths, the similarity of paths is defined by Equation (6.1). In this equation, Si,j represents similarity between path i and j. Li,j represents overlapped length between path i and j. Li represents path length of path i. Similarity becomes 1 when two paths overlap completely. Similarity denotes 0 when two paths have no part of overlapping. Si , j

Li , j Li ˜ L j

(6.1)

Similarity of paths by proposed algorithm is 0.09 while similarity of paths founded by conventional k-ordered Dijkstra's algorithm is 0.2 on average. Smaller similarity indicates larger dissimilarity. This result indicates the proposed algorithm finds more dissimilar paths than the

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conventional k-ordered Dijkstra's algorithm. Figure 6.2 (a) shows a trajectory colliding with a building structure around a turning point in the boiler building. (b) indicates that the trajectory avoids collision with the building structure after applying collision avoidance method which revises the kinematic parameter d1 in Type 1 in Fig.5.1(a). The proposed algorithm was applied to find paths to carryout/carry-in tasks for pipe replacement of an existing boiler building in a power plant in Germany. Figure 6.3 indicates the second turning point of path #1 in Fig. 6.1 and its picture in the boiler building. Purple cylinder in Fig.6.3(a) denotes the found path. 7. Conclusions Novel fast multiple paths finding algorithm is proposed to carry-out/carry-in tasks in a power plant. Our algorithm fulfil following requirements. (1)The algorithm computes less than one minute for one path finding in order to realize interactive user interface. (2)The algorithm finds dissimilar multiple paths with considering the space margins and the number of the turning points. (3)The algorithm generates collision avoidance pose trajectories around turning points with simulating crane suspension. The proposed algorithm has been applied to the pipe replacement of existing boiler buildings in two power plants.

⁗⁠⁖‒⁢⁡⁛⁠⁦

Table 6.1 Path Evaluation

―‧ ―… ―‣

―‥

―․ ⁥⁦⁓⁤⁦‒⁢⁡⁛⁠⁦

# The number Space of turning margin

Path length

1

3

2.2

162.0

2

5

2.2

163.6

3

6

2.1

170.6

4

6

1.8

163.6

5

8

2.6

168.5

Fig. 6.1 Experiment result

(a) Colliding trajectory

(b) Revised trajectory for collision avoidance

Fig. 6.2 Collision avoided trajectory around turning point

References [1]http://www.3ds.com/, Dassault systems [2]http://www.informatix.co.jp/top/profile_e.html, informatrix [3]http://www.autodesk.com/suites/plant-design-suite/overview, Autodesk [4]http://www.aveva.com/en/Products_and_Services/AVEVA_for_Plant/AV EVA_for_EPCs.aspx, Aveva [5]http://www.bentley.com/en-US/Products/microstation+product+line, Bentley [6]http://www.intergraph.com/ppm/3dmv.aspx, Intergraph [7]Dijkstra, E.W. (1959). A note on two problems in connexion with graphs. In Numerische Mathematik, 1 (1959), S. 269 ̚ 271. [8]Hart, P. E.; Nilsson, N. J.; Raphael, B. (1968). "A Formal Basis for the Heuristic Determination of Minimum Cost Paths". IEEE Transactions on Systems Science and Cybernetics SSC4 (2): pp. 100–107. PDF [9]Hiroshi Matsuura, A proposal of k shortest simple path algorithm to minimize computational complexity, IEICE Tech. Rep., vol. 110, no. 341, IN2010-107, pp. 57-62, Dec. 2010. [10]Tomás Lozano-Pérez, Michael A. Wesley, An Algorithm for Planning Collision-Free Paths Among Polyhedral Obstacles, Communications of the ACM, Volume 22 Issue 10, Oct. 1979, Pages 560-570 [11]RODNEY A. BROOKS, 1983, Solving the Find-Path Problem by Good Representation of Free Space, IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS, VOL. SMC-13, NO. 3, MARCH/APRIL [12]Jacob T Schwartz, 1983, On the “piano movers” problem. II. General techniques for computing topological properties of real algebraic manifolds, Advances in Applied Mathematics, 4/3: 298–351 [13]Ratliff, N., Bagnell, J. A., 2006, Zinkevich, M. A., Maximum Margin Planning, International Conference on Machine Learning. [14]Svestka, P., Latombe, J. C., Overmars Kavraki, L.E., 1996, Probabilistic roadmaps for path planning in high-dimensional configuration spaces, IEEE Transactions on Robotics and Automation, 12/4:566-580. [15]LaValle, S. M., and Kuffner, J. J., 1999, Randomized kinodynamic planning, In Proceedings IEEE International Conference on Robotics and Automation, 473-479.

(a) found path (blue cylinder)

(b) Picture of (a)

Fig. 6.3 the second turning point of path #1 in Fig. 6.1

[16]Diankov,R., and Kuffner., J., 2007, Randomized Statistical Path Planning, In Proc. of the 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems, TuA1.1. [17] Nagai, S., Kanesige, A., Ueki, S., 2011, Three-Dimensional Obstacle Avoidance Online Path-Planning Method for Autonomous Mobile Overhead Crane, In Proc. of 2011 International Conference on Mechatronics and Automation, 7-10. [18] Gross, M., James, D., 2008, Elevation Cable Modelling for Interactive Simulation of Cranes,. European SIGGRAPH Symposium on Computer Animation, [19] Felez, J., Maroto, J., Cabanellas, M. J., Mera, M., J., 2013, Simulation: Trans. of the Society for Modeling and Simulation International, 89(9), 1099-1114. [20] Diankov, R., Kuffner, J., 2007, Proc. of the 2007 iEEE/RSJ Int. COnf on Intelligent Robots and Systems, Snn Diego, CA, USA, Oct 29-Nov 2, TuA1.1. 1-6. [21] Fragkopoulos, C., Graer, A., 2011, Dynamic efficent collision checking method of robot amr paths in configration space, 2001 iEE/ASME Int. Conf. on Advanced Intelligent Mechatronics, Budapest, Hungary, July 37, 784-789.